We identify the null orbit 𝒩 = −1/2 · 2ᵏ: k ∈ ℤ of the map f (x) = 3x+1 and use it to organise the divergence obstruction of the Syracuse map. The null x₀ = −1/2 is simultaneously the algebraic fixed point of f, the value of Σ3ⁱ under analytic continuation, and (up to the transparent factor 2) the unique 2-adic fixed point sustaining maximal expansion. The cycle problem is constrained by Baker's theorem and theoretical lower bounds on cycle length; the null orbit does not participate in the cycle Diophantine equation (the pure map's fixed-point equation and the Syracuse cycle equation are algebraically independent). The divergence problem is reformulated through structural arguments centred on 𝒩. Three boundary results (B) identify the non-closure interfaces of the Serie I tool chain: Baker bounds do not control numerator divisibility; SU (2) -density does not imply deterministic orbital equidistribution; and the self-referential remainder cannot be controlled by assuming the surplus it is meant to prove. Three concrete closure targets are formulated: a cycle numerator principle, an orbital co-length principle, and a low-altitude occupation principle. The framework should be read as a localisation of the Collatz frontier, not as a closure of it. Serie I · v0. 6.
Ricardo Hernández Reveles (Wed,) studied this question.